Four-phase single-capillary stepwise model for kinetics in arterial spin labeling MRI

Abstract

An extended model for extracting measures of brain perfusion from pulsed arterial spin labeling (ASL) data while considering transit effects and restricted permeability of capillaries to blood water is proposed. We divided the time course of the signal difference between control and labeled images into four phases with respect to the arrival time of labeled blood water at the voxel of interest (t(A)), transit time through the arteries in the voxel (t(ex)), and duration of the bolus of labeled spins (tau). Dividing the labeled slab of blood water into many discrete segments, and adapting numerical integration methods allowed us to conveniently model restricted capillary-tissue exchange based on a modified distributed parameter model. We compared this four-phase single-capillary stepwise (FPSCS) model with models that treat water as a freely diffusible tracer, using both simulations and experimental ASL brain imaging data at 1.5T from eight healthy subjects (24-80 years old). The FPSCS model yielded less errors in the least-squares sense in fitting brain ASL data in comparison with freely diffusible tracer models of water (P = 0.055). These results imply that restricted permeability of capillaries to water should be considered when brain ASL data are analyzed.

FIG. 1

A numerical method for calculating water exchange in a single-capillary stepwise model. Blood flows into the voxel through arterioles, and flows out of the voxel through venules. In arteries, arterioles, and veins there is no exchange of water between blood and tissue. The tissue compartment is therefore only represented around the capillary. a: The slab of labeled water has completely entered the capillary space (t > Tex + τ). It is divided into K segments with a thickness of Δt_seg = τ/K. The water exchange for each of the segments was calculated by the technique of sliding the segment from the capillary entry downstream toward venous outflow in a stepwise fashion as if the segment suddenly slipped one segment length downstream. During each moving step, water exchange occurs via diffusion. See Eq. [A8] for the numerical equation of ΔMe(t). b: Only a part of the labeled water slab has entered the capillary space (T_ex < t < T_ex + τ). The labeled water in the capillary is divided into K segments with Δt_seg = (t − Tex)/K. The contribution from the labeled water, which is still in the arterial space, is denoted as ΔM_a(t) (Eq. [3]). When the slab of labeled water has completely entered the capillary space, as illustrated in a, ΔM_a(t) = 0.

FIG. 2

a: ASL signal simulations for different values of capillary permeability (PS_v), showing a faster ASL signal decay as permeability increases. b: Decomposition of the ASL signal into its different components occupying arterial, capillary, and extravascular spaces. This highlights the delays from the arrival of labeled water in an image voxel to the arrival in capillary space and eventually perfusion into extravascular space.

FIG. 3

Parametric images of flow, PS_v, and SFE from a 55-year-old woman, obtained with the FPSCS model and a time curve of ASL values measured in cortical gray matter. The fits of the ASL time curve based on the FPSCS (solid lines) and FPOCK (dotted lines) models are also shown for comparison.